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ee2:task_ti7loik6aurfewkb_with_calculation [2024/07/01 13:20]
mexleadmin angelegt 		ee2:task_ti7loik6aurfewkb_with_calculation [2024/07/03 08:24] (aktuell)
mexleadmin
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-{{tag>magnetostatic flux_density exam_ee2_SS2021}}{{include_n>1000}}+{{tag>magnetostatic flux_density exam_ee2_SS2021}}{{include_n>1170}}
    
-#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~ Resistance of a Wire by Resistivity\\+#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~ Magnetic Flux Density\\
 <fs medium>(written test, approx. 6 % of a 120-minute written test, SS2021)</fs> #@TaskText_HTML@# <fs medium>(written test, approx. 6 % of a 120-minute written test, SS2021)</fs> #@TaskText_HTML@#
  
-Several parallel conductors are projecting out of the plane. \\ +An electric motor is operated for experiments in the laboratory. An alternating current with an amplitude of $\hat{I} = 100~\rm A$ is operated. \\ 
-The same current $|I|$ flows through all the conductors in different directions (see image below). \\ +You stand next to it and think about whether you have any health problems to worry about. The figure below shows the top view of the laboratory with the supply line between $\rm A$ and $\rm B$.  
-Sketch at least 10 field lines of the magnetic field strength $\vec{H}$ in such a way that the different properties of the field lines (e.g. direction and density) can be seen. +
  
-{{drawio>ee2:76ksbc114ylxftfldiagram1.svg}}+$\mu_{0} = 4\pi\cdot 10^{-7} {{\rm Vs}\over{\rm Am}}$, $\mu_{r}=1$
  
 +{{drawio>ee2:ti7LOik6AUrfewKbdiagram1.svg}}
  
-#@ResultBegin_HTML~1~@# +a) What is the highest magnetic flux density through the line in your body? (3 points)  
 + 
 +#@HiddenBegin_HTML~ti7LOik6AUrfewKb_11,Path~@# 
 + 
 +The magnetic field strength for a conducting wire is given as: 
 + 
 +\begin{align*} 
 + H &= {{I}\over{2\pi \cdot r}} 
 +\end{align*} 
 + 
 +The magnetic flux density $B$ is given as: $B = \mu_0 \mu_r H$ 
 + 
 +Here, the maximum current is $\hat{I} = 100~\rm A$ and the distance to the cable is $r = \sqrt{(0.1 {~\rm m})^2 + (0.4 {~\rm m})^2}= 0.412... ~\rm m$. 
 + 
 +Therefore: 
 +\begin{align*} 
 + B &= 4\pi\cdot 10^{-7} {{\rm Vs}\over{\rm Am}} \cdot 1 \cdot {{100 ~\rm A}\over{2\pi \cdot 0.412... ~\rm m}} 
 +\end{align*} 
 +#@HiddenEnd_HTML~ti7LOik6AUrfewKb_11,Path ~@# 
 + 
 +#@HiddenBegin_HTML~ti7LOik6AUrfewKb_12,Result~@# 
 +$B = 49 ~\mu \rm T$ 
 +#@HiddenEnd_HTML~ti7LOik6AUrfewKb_12,Result~@# 
 + 
 +b) The limit value for the magnetic flux density at the frequency used is $B_0 = 100~\rm \mu T$. \\ 
 +At what distance around the conductor is this value exceeded? (3 points, independent)  
 + 
 +#@HiddenBegin_HTML~ti7LOik6AUrfewKb_21,Path~@# 
 + 
 +The formula for the magnetic field strength can be rearranged: 
 +\begin{align*} 
 + H &= {{I}\over{2\pi \cdot r}} \\ 
 + r &= {{I}\over{2\pi \cdot H}} \\ 
 +\end{align*} 
 + 
 +Again, the magnetic flux density $B$ is given as: $B = \mu_0 \mu_r H$ \\ 
 +Therefore: 
 +\begin{align*} 
 + r &= \mu_0 \mu_r                               {{ I   }\over{2\pi \cdot B}}  \\ 
 +   &= 4\pi\cdot 10^{-7} {{\rm Vs}\over{\rm Am}} {{100 ~\rm A}\over{2\pi \cdot 100\cdot 10^{-6} {~\rm T}}}  \\ 
 +\end{align*} 
 +#@HiddenEnd_HTML~ti7LOik6AUrfewKb_21,Path ~@# 
 + 
 +#@HiddenBegin_HTML~ti7LOik6AUrfewKb_22,Result~@# 
 +$r =   0.2~\rm m$ 
 +#@HiddenEnd_HTML~ti7LOik6AUrfewKb_22,Result~@#
  
-  * high density of field lines near the conductors 
-  * direction of the field lines given by the right-hand rule 
-  * magnetic field has closed field lines 
-  * resulting field given by superposition of field lines  
-{{drawio>ee2:76ksbc114ylxftfl_solution.svg}} 
-#@ResultEnd_HTML~1~@# 
  
 #@TaskEnd_HTML@# #@TaskEnd_HTML@#